In an exhaust system of an internal combustion engine, various sensors such as an air-fuel ratio sensor (A/F sensor) for detecting an air-fuel ratio in the exhaust gas are provided. When inhibitors such as particulate matters in the exhaust gas adhere to a detection unit of these kinds of sensors, the sensors become unable to obtain accurate detection values, and thereby the detection accuracy is deteriorated. As a technique for dealing with this, in Patent Reference-1, there is described a technique which determines, at the time when an operation state of a engine is a static state, whether an output value of an oxygen sensor is smaller than a predetermined value or larger than the predetermined value, and which burns up the particulate matters by increasing temperature of an electrical heater for heating up a detection element of the oxygen sensor at the time when the output value is larger than the predetermined value. In Patent References-2 and -3, there are also described technique which relates to the present invention.    Patent Reference-1: Japanese Patent Application Laid-open under No. H11-82112    Patent Reference-2: Japanese Patent No. 3744486    Patent Reference-3: Japanese Patent No. 3958755